feat: 扩展天文计算能力
- 新增日食、月食、本地可见性、中心线、半影区域、SVG 图示与沙罗周期信息 - 新增行星冲合、留、方照、物理星历、视直径、相位、亮肢角、轨道节点等计算 - 新增木星伽利略卫星位置、现象与接触事件计算 - 新增恒星星表、星座判定、自行修正与观测辅助能力 - 新增 coord、formula、orbit、sundial、lite/sun、lite/moon 等扩展包 - 完善农历年号、月相英文别名、视差角、大气质量、折射、日晷与双星计算 - 增加 NASA、JPL Horizons、IMCCE 等回归测试数据与基线测试 - 重构基础算法文件组织，补充大量公开 API 注释和语义回归测试 - 更新中文和英文 README，补充示例、精度说明、SVG 配图
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package basic
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import (
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"math"
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"b612.me/astro/planet"
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. "b612.me/astro/tools"
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)
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var orbitJ2000Obliquity = EclipticObliquity(orbitReferenceJD, false)
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// OrbitHeliocentricXYZJ2000 返回日心 J2000 平黄道直角坐标，单位 AU。
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func OrbitHeliocentricXYZJ2000(jd float64, elements OrbitElements) Vector3 {
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trueAnomaly, radius, resolved, ok := orbitTrueAnomalyAndRadius(jd, elements)
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if !ok {
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nan := math.NaN()
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return Vector3{nan, nan, nan}
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}
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ascendingNode := resolved.Omega * rad
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argumentLatitude := resolved.W*rad + trueAnomaly
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inclination := resolved.I * rad
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sinAscendingNode, cosAscendingNode := math.Sincos(ascendingNode)
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sinArgumentLatitude, cosArgumentLatitude := math.Sincos(argumentLatitude)
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sinInclination, cosInclination := math.Sincos(inclination)
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return Vector3{
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radius * (cosAscendingNode*cosArgumentLatitude - sinAscendingNode*sinArgumentLatitude*cosInclination),
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radius * (sinAscendingNode*cosArgumentLatitude + cosAscendingNode*sinArgumentLatitude*cosInclination),
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radius * sinArgumentLatitude * sinInclination,
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}
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}
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// OrbitHeliocentricEclipticJ2000 返回日心 J2000 平黄道球坐标，单位度/AU。
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func OrbitHeliocentricEclipticJ2000(jd float64, elements OrbitElements) (lon, lat, distance float64) {
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return orbitVectorToEcliptic(OrbitHeliocentricXYZJ2000(jd, elements))
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}
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// OrbitHeliocentricXYZ 返回日心历元黄道直角坐标，单位 AU。
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func OrbitHeliocentricXYZ(jd float64, elements OrbitElements) Vector3 {
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return eclipticVectorAtReferenceEpoch(OrbitHeliocentricXYZJ2000(jd, elements), orbitReferenceJD, jd)
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}
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// OrbitHeliocentricEcliptic 返回日心历元黄道球坐标，单位度/AU。
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func OrbitHeliocentricEcliptic(jd float64, elements OrbitElements) (lon, lat, distance float64) {
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return orbitVectorToEcliptic(OrbitHeliocentricXYZ(jd, elements))
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}
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// OrbitGeocentricXYZJ2000 返回地心 J2000 平黄道直角坐标，单位 AU。
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func OrbitGeocentricXYZJ2000(jd float64, elements OrbitElements) Vector3 {
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objectVector := OrbitHeliocentricXYZJ2000(jd, elements)
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earthVector := earthHeliocentricVectorJ2000(jd)
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return Vector3{
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objectVector[0] - earthVector[0],
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objectVector[1] - earthVector[1],
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objectVector[2] - earthVector[2],
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}
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}
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// OrbitGeocentricEclipticJ2000 返回地心 J2000 平黄道球坐标，单位度/AU。
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func OrbitGeocentricEclipticJ2000(jd float64, elements OrbitElements) (lon, lat, distance float64) {
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return orbitVectorToEcliptic(OrbitGeocentricXYZJ2000(jd, elements))
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}
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// OrbitGeocentricXYZ 返回地心历元黄道直角坐标，单位 AU。
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func OrbitGeocentricXYZ(jd float64, elements OrbitElements) Vector3 {
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objectVector := OrbitHeliocentricXYZ(jd, elements)
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earthVector := earthHeliocentricVectorOfDate(jd)
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return Vector3{
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objectVector[0] - earthVector[0],
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objectVector[1] - earthVector[1],
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objectVector[2] - earthVector[2],
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}
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}
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// OrbitGeocentricEcliptic 返回地心历元黄道球坐标，单位度/AU。
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func OrbitGeocentricEcliptic(jd float64, elements OrbitElements) (lon, lat, distance float64) {
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return orbitVectorToEcliptic(OrbitGeocentricXYZ(jd, elements))
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}
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// OrbitGeocentricEquatorialJ2000 返回地心 J2000 平赤道球坐标，单位度/AU。
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func OrbitGeocentricEquatorialJ2000(jd float64, elements OrbitElements) (ra, dec, distance float64) {
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vector := rotateEclipticToEquatorial(OrbitGeocentricXYZJ2000(jd, elements), orbitJ2000Obliquity)
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return orbitVectorToEquatorial(vector)
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}
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// OrbitGeocentricEquatorial 返回地心历元平赤道球坐标，单位度/AU。
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func OrbitGeocentricEquatorial(jd float64, elements OrbitElements) (ra, dec, distance float64) {
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vector := rotateEclipticToEquatorial(OrbitGeocentricXYZ(jd, elements), EclipticObliquity(jd, false))
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return orbitVectorToEquatorial(vector)
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}
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// OrbitAstrometricGeocentricXYZJ2000 返回光行时修正后的地心 J2000 平黄道直角坐标，单位 AU。
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func OrbitAstrometricGeocentricXYZJ2000(jd float64, elements OrbitElements) Vector3 {
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if !isFinite(jd) {
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nan := math.NaN()
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return Vector3{nan, nan, nan}
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}
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earthVector := earthHeliocentricVectorJ2000(jd)
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lightTime := 0.0
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result := Vector3{}
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for i := 0; i < 8; i++ {
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objectVector := OrbitHeliocentricXYZJ2000(jd-lightTime, elements)
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result = Vector3{
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objectVector[0] - earthVector[0],
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objectVector[1] - earthVector[1],
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objectVector[2] - earthVector[2],
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}
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nextLightTime := lightTimeDaysPerAU * orbitVectorNorm(result)
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if math.Abs(nextLightTime-lightTime) < 1e-12 {
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break
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}
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lightTime = nextLightTime
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}
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return result
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}
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// OrbitAstrometricGeocentricEquatorialJ2000 返回光行时修正后的地心 J2000 赤道坐标，单位度/AU。
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func OrbitAstrometricGeocentricEquatorialJ2000(jd float64, elements OrbitElements) (ra, dec, distance float64) {
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vector := rotateEclipticToEquatorial(OrbitAstrometricGeocentricXYZJ2000(jd, elements), orbitJ2000Obliquity)
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return orbitVectorToEquatorial(vector)
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}
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// OrbitApparentGeocentricEcliptic 返回光行时与章动修正后的地心视黄道坐标，单位度/AU。
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func OrbitApparentGeocentricEcliptic(jd float64, elements OrbitElements) (lon, lat, distance float64) {
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vectorDate := eclipticVectorAtReferenceEpoch(OrbitAstrometricGeocentricXYZJ2000(jd, elements), orbitReferenceJD, jd)
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lon, lat, distance = orbitVectorToEcliptic(vectorDate)
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if math.IsNaN(lon) {
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return math.NaN(), math.NaN(), math.NaN()
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}
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lon = Limit360(lon + Nutation2000Bi(jd))
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return lon, lat, distance
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}
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// OrbitApparentGeocentricEquatorial 返回光行时与章动修正后的地心视赤道坐标，单位度/AU。
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func OrbitApparentGeocentricEquatorial(jd float64, elements OrbitElements) (ra, dec, distance float64) {
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lon, lat, distance := OrbitApparentGeocentricEcliptic(jd, elements)
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if math.IsNaN(lon) {
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return math.NaN(), math.NaN(), math.NaN()
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}
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ra, dec = LoBoToRaDec(jd, lon, lat)
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return ra, dec, distance
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}
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// OrbitApparentTopocentricEquatorial 返回光行时、章动与站心修正后的视赤道坐标，单位度/AU。
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func OrbitApparentTopocentricEquatorial(jd, observerLon, observerLat, observerHeight float64, elements OrbitElements) (ra, dec, distance float64) {
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geocentricRA, geocentricDec, geocentricDistance := OrbitApparentGeocentricEquatorial(jd, elements)
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if math.IsNaN(geocentricRA) {
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return math.NaN(), math.NaN(), math.NaN()
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}
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geocentricVector := orbitEquatorialVector(geocentricRA, geocentricDec, geocentricDistance)
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observerVector := orbitObserverEquatorialVectorOfDate(TD2UT(jd, false), observerLon, observerLat, observerHeight)
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topocentricVector := Vector3{
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geocentricVector[0] - observerVector[0],
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geocentricVector[1] - observerVector[1],
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geocentricVector[2] - observerVector[2],
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}
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return orbitVectorToEquatorial(topocentricVector)
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}
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func earthHeliocentricVectorOfDate(jd float64) Vector3 {
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return eclipticCartesian(
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planet.WherePlanet(-1, 0, jd),
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planet.WherePlanet(-1, 1, jd),
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planet.WherePlanet(-1, 2, jd),
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)
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}
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func earthHeliocentricVectorJ2000(jd float64) Vector3 {
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return eclipticVectorAtReferenceEpoch(earthHeliocentricVectorOfDate(jd), jd, orbitReferenceJD)
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}
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func orbitVectorToEcliptic(vector Vector3) (lon, lat, distance float64) {
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distance = orbitVectorNorm(vector)
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if math.IsNaN(distance) || math.IsInf(distance, 0) {
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return math.NaN(), math.NaN(), math.NaN()
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}
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if distance == 0 {
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return 0, 0, 0
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}
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lon = Limit360(math.Atan2(vector[1], vector[0]) * deg)
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lat = math.Asin(orbitClampUnit(vector[2]/distance)) * deg
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return lon, lat, distance
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}
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func orbitVectorToEquatorial(vector Vector3) (ra, dec, distance float64) {
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distance = orbitVectorNorm(vector)
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if math.IsNaN(distance) || math.IsInf(distance, 0) {
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return math.NaN(), math.NaN(), math.NaN()
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}
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if distance == 0 {
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return 0, 0, 0
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}
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ra = Limit360(math.Atan2(vector[1], vector[0]) * deg)
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dec = math.Asin(orbitClampUnit(vector[2]/distance)) * deg
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return ra, dec, distance
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}
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func orbitEquatorialVector(ra, dec, distance float64) Vector3 {
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cosDec := Cos(dec)
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return Vector3{
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distance * cosDec * Cos(ra),
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distance * cosDec * Sin(ra),
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distance * Sin(dec),
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}
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}
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func orbitObserverEquatorialVectorOfDate(jdUT, observerLon, observerLat, observerHeight float64) Vector3 {
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localApparentSiderealLongitude := Limit360(ApparentSiderealTime(jdUT)*15 + observerLon)
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observerScaleAU := Sin(0.0024427777777)
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rhoCosPhiPrime := pcosi(observerLat, observerHeight)
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rhoSinPhiPrime := psini(observerLat, observerHeight)
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return Vector3{
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observerScaleAU * rhoCosPhiPrime * Cos(localApparentSiderealLongitude),
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observerScaleAU * rhoCosPhiPrime * Sin(localApparentSiderealLongitude),
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observerScaleAU * rhoSinPhiPrime,
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}
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}
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func orbitVectorNorm(vector Vector3) float64 {
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return math.Sqrt(vector[0]*vector[0] + vector[1]*vector[1] + vector[2]*vector[2])
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}
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func orbitClampUnit(value float64) float64 {
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if value > 1 {
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return 1
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}
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if value < -1 {
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return -1
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}
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return value
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}
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